The Question is from neet-physics units-and-measurement conversion-of-units-for-one-system-to-another, and it was created by the author NAGA SAI

Question

Out of the following which pair of quantities do not have same dimensions

NAGA SAI · Accepted Answer

## CORE INFORMATION
✓ **Answer**: D
## CONCEPT FRAMEWORK
	**Primary Concept**: Dimensional Analysis
	**Related Topics**: Physical Quantities, Units and Measurements
	**Prerequisites**: Knowledge of basic physical quantities and their dimensions (M, L, T)
## SOLUTION PATHWAY
**Given Information**:
	List of pairs of physical quantities.
	Need to determine which pair does not have the same dimensions.
**Method & Steps**:
	1. Find the dimensions of each quantity.
		Reasoning: Dimensions are fundamental units that describe a physical quantity.
		Formula/Rule: Use the formulas associated with the quantity to derive dimensions.
	2. Compare the dimensions of quantities in each pair.
		Working: 
		A. Planck's constant (h) [ML²T⁻¹] and Angular Momentum (L) [ML²T⁻¹] - Same Dimensions.
		B. Work (W) [ML²T⁻²] and Energy (E) [ML²T⁻²] - Same Dimensions.
		C. Pressure (P) [ML⁻¹T⁻²] and Young's Modulus (Y) [ML⁻¹T⁻²] - Same Dimensions.
		D. Torque (τ) [ML²T⁻²] and Moment of Inertia (I) [ML²] - Different Dimensions.
	3. Identify the pair with differing dimensions
		Result: Torque and Moment of Inertia have different dimensions.
		Verification: Based on the dimensional analysis.
 ## OPTION ANALYSIS
[A] :x: Planck’s constant and angular momentum have the same dimensions (ML²T⁻¹).
[B] :x: Work and energy have the same dimensions (ML²T⁻²).
[C] :x: Pressure and Young’s modulus have the same dimensions (ML⁻¹T⁻²).
[D] ✓: Torque (ML²T⁻²) and moment of inertia (ML²) have different dimensions.
 ## LEARNING AIDS
	**Common Mistakes**:
		1. Incorrectly deriving dimensions: Double-check the formulas and basic dimensions.
		2. Confusing different quantities: Be careful to use the correct formula for each quantity.
	**Quick Tips**:
		1. Remember the basic dimensions: [M] for mass, [L] for length, [T] for time.
		2. Use known formulas: To derive dimensions from physical quantities.

NAGA SAI · Answer

Planck’s constant and angular momentum

NAGA SAI · Answer

Work and energy

NAGA SAI · Answer

Pressure and Young’s modulus

NAGA SAI · Answer

The correct Option is "Torque and moment of inertia"

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